USRE42546E1 - Method and system for target localization - Google Patents
Method and system for target localization Download PDFInfo
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- USRE42546E1 USRE42546E1 US11/318,398 US31839805A USRE42546E US RE42546 E1 USRE42546 E1 US RE42546E1 US 31839805 A US31839805 A US 31839805A US RE42546 E USRE42546 E US RE42546E
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S3/00—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received
- G01S3/80—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received using ultrasonic, sonic or infrasonic waves
- G01S3/802—Systems for determining direction or deviation from predetermined direction
- G01S3/808—Systems for determining direction or deviation from predetermined direction using transducers spaced apart and measuring phase or time difference between signals therefrom, i.e. path-difference systems
- G01S3/8086—Systems for determining direction or deviation from predetermined direction using transducers spaced apart and measuring phase or time difference between signals therefrom, i.e. path-difference systems determining other position line of source
Definitions
- the present inventions relate to localization of an object or target of interest.
- Track Motion Analysis It is often desirable to track one object from another object to determine if the tracked object will intercept the tracking object, or at what point in time will the tracked object be at it closest approach to the tracking object, sometimes referred to in the art as “Target Motion Analysis.”
- a vessel afloat in the presence of subsea or partially submerged obstacles would need to know where those obstacles are in order to avoid hitting those obstacles.
- such systems have been proposed in the art to avoid collisions with other vessels, collisions with such as icebergs, and collisions with submerged objects sufficient to cause damage such as ledges, seamounts, or reefs.
- U.S. Pat. No. 6,199,471 issued to Perruzzi, et al. for a “Method And System For Determining The Probable Location Of A Contact” teaches a method and a system for determining a weapon firing strategy for an evading target.
- Perruzzi '471 comprises the steps of sensing the motion of the target, analyzing the motion of the target, providing a weapon employment decision aid, determining the evasion region for the target using the weapon employment decision aid and the analyzed motion, visually displaying the evasion region, feeding operator knowledge about evading target, and generating a representation of the probability of the location of the evading target.
- U.S. Pat. No. 5,867,256 to Van Rheeden for “Passive Range Estimation Using Image Size Measurements” teaches a range estimation system and method which comprises a data base containing data for identification of certain targets and data for estimating the initial range to each of the targets as a function of the observed dimensions of the targets.
- a sensor ( 1 ) observes a scene containing a target a plurality of spaced apart times while the sensor is moving relative to the target to provide data from each observation of the scene relating to the dimensions of the target within the scene.
- the remaining range to the target is estimated from the observed dimensions of the target from the range traveled since a prior estimation of range and from a prior estimation of the remaining range to the target.
- the sensor ( 1 ) provides electrical signals representing the observed scene ( 3 ) and can be a visible light or infrared sensor.
- a computer ( 9 ) is used to identify the target from the data base, estimate the initial range to the target and estimate the remaining range from the range traveled between successive observations of the scene and the change of dimensions of the target in the observed scene.
- tracking methods would preferably fix a boundary on the range to the tracked object quickly while using a minimum amount of data, preferably passive data. Further, it is preferable to calculate the bearing of the tracked object with respect to the tracking object at a point of closest approach, along with calculating a time to that closest approach, independent of other position data.
- the AN/SQQ-89(V) UFCS (Navy) surface ship ASW Fire Control System currently uses the Manual Adaptive Target Estimator (MATE) and Maximum Likelihood Estimator (MLE) algorithms to determine target position. These algorithms require substantially more data than the present inventions to obtain their results.
- the MATE algorithm requires operator based estimates, and systematic manual manipulation of the data to arrive at a position, course and speed estimate of the target.
- the MLE algorithm also requires limited operator input to arrive at a statistically based estimate of position, course and speed of the target. Both of these algorithms require a substantial amount of data, approximately fifteen to twenty data points, to arrive at a stable solution.
- FIG. 1 is an exemplary Cartesian plot of a target, an ownship, and various vectors related to the two, in a geographic reference frame;
- FIG. 2 is an exemplary Cartesian plot of a target, an ownship, and various vectors related to the two, in a reference frame relative to an ownship's position;
- FIG. 3 is an exemplary Cartesian plot showing determination of target maneuvers and noise in the system.
- FIG. 4 is a schematic representation of an exemplary system.
- the present inventions comprise a method of providing bounds for approximations for tracking an object such as target 2 with respect to a first object such as ownship 1 .
- the present inventions comprise methods for creating calculations useful for bounding tracking sensor localization using a substantially minimum amount of data, in a preferred embodiment especially using passively obtained data as that term is understood by those of ordinary skill in the target detection arts.
- the methods comprise calculating relative bearing at a closet point of approach (“CPA”) and time of CPA independently of other position data, estimating target motion analysis (“TMA”) solution noise, and detecting contact maneuvers.
- the methods of the present inventions may be used to conduct passive TMA using symmetries associated with two different views of a problem to be solved, e.g. two reference frames and two points of interest.
- a first of these frames, geographic frame of reference 100 is shown in FIG. 1 and second frame of reference, relative frame of reference 200 , is shown in FIG. 2 .
- the “points of interest” include a first physical object such as ownship 1 , and a second, target 2 , such as second vessel.
- ownship means a first reference point that is not a target, i.e. the vessel making the calculations.
- Each of these points of interest may be in motion or stationary, and, if in motion, may be in motion in different planes with respect to each other.
- Target motion analysis or TMA means that the course and speed for target 2 , which may initially be unknown, are resolved as well as the range to and bearing of target 2 at or for a predetermined time frame with respect to ownship 1 .
- bearing at CPA, time of CPA, a minimum range to the target with associated course and speed for the minimum range only as a limiting condition, and an initial estimate of the target's true range, course and speed may be determined.
- target 2 may be another vessel, an iceberg, a submerged object such as a ledge or reef, or the like, assuming that target 2 emits a signal that can be detected by a passive sensor for the passive solution.
- the methods of the present inventions may be used with partially or fully submerged features such as rocks or debris, floating materials, stationary materials, and the like, or combinations thereof, especially if the presence of such features may be determined, but a measurement of range to the feature may be lacking in the detection device that detects the feature.
- active as well as passive data may be used in the present inventions' methods, in which case any single active signal may be used to determine a range value which can then be used in conjunction with passive data to fully resolve range, bearing, course and speed.
- the present inventions' methods comprise obtaining at least three bearing and time data points for a first estimate, e.g. at time points t 1 , t 2 , t 3 , t 4 . These data are used to isolate a passive TMA estimate based on a single leg of time tagged, bearings only data, i.e. no maneuvering of the first point of interest such as ownship 1 is required to obtain a passive estimate. Further, the present inventions' methods comprise a closed form expression for an estimate that may be resolved in a single iteration as opposed to prior art methods such as those using first order statistical solutions.
- the present inventions' methods utilize velocity vectors of the two items of interest, i.e. vector 13 and estimated vector 30 . These velocity vectors, when arranged to determine their vector difference, form one side 52 , 53 of a parallelogram as well as a diagonal of that parallelogram, shown as darkened portion 51 of vector 13 .
- the perpendicular distances to respective opposite sides of the parallelogram change in a predetermined fashion, i.e.
- the corresponding length of the diagonal must increase by an amount equal to the relative velocity of ownship 1 and target 2 multiplied by the new elapsed time value for the second course crossing minus t 0 , such that perpendicular distance to opposing sides increases by an amount proportional to twice the range at CPA. Additionally, the greater the difference between values of adjacent vertices, the smaller the perpendicular distance to opposing sides.
- successive time-lagged bearing lines e.g. lines 11 and 12
- solution parabola 15 in geometric reference frame 100 for substantially all geometries involving two points of interest 1 , 2 , where each of the points of interest 1 , 2 maintains a substantially constant respective course and speed over a time period used for obtaining bearing measurements.
- Solution parabola 15 is formed by recognizing that each of the bearing lines 11 , 12 , 13 , 20 , 30 in geographic reference frame 100 are tangent to solution parabola 15 at a predetermined, unique point.
- solution parabola 15 will be fixed in geographic reference frame 100 , and each data set to be gathered will generate one and one only solution parabola 15 , although different data sets may generate the same solution parabola 15 .
- the value of the bearing at the CPA, e.g. angle 50 ′ is constant for potential ranges at CPA.
- the difference vector of each potential velocity vector pair i.e.
- velocity vector for target 2 and velocity vector of ownship 1 remains parallel for all geometries involving those two points of interest where each point of interest 1 , 2 maintains its respective course and speed at a constant value during the time of measurements and calculation.
- This allows calculation of bearing at CPA, time of CPA, and minimum range at CPA, with data comprising a single leg of passive, time tagged bearings. Further, this allows estimates of TMA solutions based on minimum range and preferred range estimates with data comprising a single leg of passive, time tagged bearings.
- the presently preferred embodiment of the present inventions' methods requires fixing an ownship 1 at rest reference frame 200 with respect to geographic reference frame 100 .
- this may be accomplished by requiring that the location of ownship 1 at an initial time t 0 is the same point in the two reference frames, e.g. 10 , and that the bearing value BRG 0 is equal to zero (as used herein “BRG” means bearing).
- an additional step may be required to reflect the original bearing line data, e.g. 13 , around a preferred bearing line in the original data set indicated by the axis of original solution parabola 15 to generate revised parabola 15 for a set of pseudo-data that reflects the course of target 2 in a reference frame for which the incident angles of courses is less than ⁇ /2.
- This situation will also require extrapolating the course of ownship 1 into a predetermined future time point and reversing the course such that the ownship arrives at the same point at the time ownship 1 crosses the course of target 2 .
- ownship 1 is located initially at point 10 .
- a first step to calculation of solution parabola 15 is to obtain three bearing data points, e.g. at times t 1 ,t 2 ,t 3 ,or t 4 , wherein the times t 1 ,t 2 ,t 3 , or t 4 at which the bearing data points were obtained are also obtained.
- Bearing data is collected in a fixed ownship reference frame such as frame 100 . At a minimum, three bearing-time data points are obtained that are relative bearings with respect to point 10 .
- Bearing data may then be translated to a moving ownship reference frame 200 .
- Two sets of data may form vectors, one set representing target 2 , e.g. 30 , and the other set representing ownship 1 , e.g. 13 , which may then cross each other at different times.
- vectors 30 and 13 may cross when target 2 appears at 0° relative bearing or 180° known bearing, or when ownship 1 appears at 0° relative to the course of target 2 or when ownship 1 appears at 180° unknown to the course of target 2 .
- bearing line 20 selects at least one potential solution point, e.g. bearing line 20 , to indicate a range at CPA.
- bearing line 20 may be selected manually by examining target geometry.
- bearing line 20 may be selected automatically such as by using artificial intelligence methods, heuristics, or the like, or a combination thereof.
- ⁇ i 0 (2)
- the formulae of the present inventions' methods may then be used to calculate a bearing fan to determine bearing data at a predetermined time in the future, independent of other position data.
- a bearing fan is a group of bearing data spaced at predetermined points in time that predicts where in bearing space target 2 will be at some point in future time, assuming that target 2 and ownship 1 maintain their current course and speed.
- the present inventions may be used to generate both relative and true bearings and time at CPA, where the time at relative bearing equals zero degrees (0°) or one hundred eighty degrees (180°).
- the formulae also provide an early estimate of minimum target ranges for any bearing, independent of other position data. Further, the formulae may be useful in many other ways, by way of example and not limitation for providing parameters useful for early target maneuver detectors or Open/Close determinations as well as estimates of a ratio of relative speed to range at CPA.
- the present inventions' methods may further be used to provide a real-time measure of the effect of noise on potential solutions.
- this real-time measure begins with a fourth data point, e.g. data point t 4 .
- the direction of the relative velocity vector 60 can be determined.
- Computer 200 may comprise any suitable computer known in the art.
- Computer 200 further comprises a processor, memory, and output device (not shown in the figures) as well as range calculation software executing within computer 200 .
- Output device 210 may comprise a display device 210 , a hard copy device 212 , or the like, or a combination thereof.
- Data sets comprising passive bearing data may be gathered such as by using one or more sensors (shown as 230 in FIG. 4 for illustration) deployed within or near ownship 1 and capable of passively obtaining a bearing to target 2 from a desired location such as ownship 1 and providing measurements related to target 2 and ownship 1 .
- Sensors 230 may comprise any suitable sensors known in the art such as passive acoustic sensors.
- the data may be passively obtained by numerous means as will be familiar to those of ordinary skill in the passive data acquisition arts. Once gathered, these data may be stored for later processing in the memory of computer 200 or in a passive bearing data collection device (not shown in the figures) that is addressably in communication with the computer. The analysis performed may occur within the computer or a portion of the computer which has been programmed to analyze the data received by the sensors.
- the computer may retrieve at least three of the stored bearing data points obtained from the bearing detector, such as from the computer's memory.
- the range calculation software may then use the three retrieved bearing data points to determine a speed contribution V os cos( ⁇ ⁇ ) of a first point of interest to a distance from a relative velocity vector over a time from t 0 to t 0 ′ in accordance with the teachings of the present inventions.
- 0 ;
- the range calculation software may then generate a representation of the probability of the location of target 1 and present that information such as on the output device.
- relative velocity vector 60 is perpendicular to the relative bearing line 20 at CPA in fixed ownship reference frame 100 , allowing for calculation of a minimum range estimate at CPA R CPA that is substantially independent of actual contact range.
- a minimum range estimate calculation is possible because a point when CPA occurs is known as is the point at which target 2 is detected at relative bearing equals ⁇ ⁇ .
- V REL R CPA [ tan ⁇ ( ⁇ ⁇ ) - tan ⁇ ( ⁇ i ) 1 + tan ⁇ ( ⁇ ⁇ ) ⁇ tan ⁇ ( ⁇ i ) - tan ⁇ ( ⁇ ⁇ ) - tan ⁇ ( ⁇ j ) 1 + tan ⁇ ( ⁇ ⁇ ) ⁇ tan ⁇ ( ⁇ j ) ] ⁇ ⁇ ⁇ t ij ( 8 )
- equation (8)
- MinR CPA V os (t ⁇ ⁇ t i )cos( ⁇ ⁇ ⁇ i ) ⁇ i
- 0 (10)
- ⁇ j current bearing measure (11) where the terms in equation (11) are defined above.
- R (CURRENTMINIMUM) R CPA(MINIMUM) /cos( ⁇ 0 ⁇ i ) (14)
- the above may be used to base target open-close on measurements calculated at the time of the decision.
- a Cartesian graph of target maneuvers and noise if more than three points are used, a series of subsequent measurements may be used to determine maneuvering of target 2 .
- a set of five or more usable bearing points may be obtained as a set of calculated points C 1 , C 2 , and C 3 in accordance with the teachings of the present inventions during times ⁇ t 1 ,t 2 ,t 3 ⁇ , ⁇ t 2 ,t 3 ,t 4 ⁇ , and ⁇ t 3 ,t 4 ,t 5 ⁇ (these time points are not shown in FIG. 3 ).
- Points C 1 , C 2 , and C 3 may be extrapolated to indicate that target 2 (shown as the dark circles in FIG. 3 ) is maneuvering in a non-linear fashion.
- the estimates may be used to determine noise or a range of noise in the readings.
- a set of five or more usable bearing points may be interpreted as a set of calculated points P 1 , P 2 , and P 3 obtained in accordance with the teachings of the present inventions during times ⁇ t 6 ,t 7 ,t 8 ⁇ , ⁇ t 7 ,t 8 ,t 9 ⁇ , and ⁇ t 8 ,t 9 ,t 10 ⁇ (these time points are not shown in FIG. 3 ).
- P 2 can be seen to have deviated from a predicted point P 2 ′, indicating that noise is present in the system.
- trends over time may therefore use these deviations to estimate the amount and effects of noise present in the system.
- analysis of deviation from a predicted point may be made with four points.
- a fifth point may then be obtained and used to determine if the deviation is random or the result of a deterministic event, e.g. a maneuvering of target 2 .
- a minimum set of points required to detect the possible presence of noise is four, and the minimum set of points required to detect the possible presence of maneuvering of target 2 is five.
- a fourth data point may be obtained.
- the fourth data point should yield the same solution, i.e., the angle to bearing at CPA relative to the heading of ownship 1 , and the time of CPA will be constant for all combinations of the three of four bearing data points.
- a deviation in the bearing at CPA relative to the heading of ownship 1 and the time of CPA represents noise in the system which can be detected by this method of calculating the angle to bearing at CPA for each potential solution.
- Prior art methods look at each bearing measurement as a unique point in “the” solution set and do not consider triplet-wise combinations of points as potential solutions to the angle at CPA, each one as valid as the other, if the bearing measurements are independent. Therefore, with the present inventions, with four data points, four potential solutions may be investigated; with five independent points, ten potential solutions may be investigated; and with six independent points, twenty potential solutions may be investigated. This is quickly recognized as the number of possible combinations of n items taken three at a time. A statistical analysis of the potential solutions may then yield trends and/or the mean and standard deviation of bearings at CPA. The mean of the bearing at CPA and the mean time of CPA are more accurate solutions of the bearing at CPA and time of CPA than any one potential solution based on a triplet of bearing measurements.
- the present inventions may allow creating twenty solutions with only six data points rather than waiting for twenty data points. Likewise, four points may be sufficient to determine that there is noise in system and calculating four bearing angle solutions at CPA provides a first order estimate of the magnitude of the noise and a first order estimate of the mean bearing at CPA and mean time of CPA.
- bearing rate curve inflection points are always plus or minus around 30° of the BRG at CPA.
Abstract
Description
tan(θβ−θi)/=VREL(tβ−ti)/RCPA|θi=0 (1)
tβ=RCPA[tan(θβ−θi)/VREL]+ti|θi=0 (2)
In these equations (1), (2), and (3),
-
- θβ is as defined in equation (3) and representatively shown as
angle 50 inFIG. 1 ; - θi is the bearing angle to the
target 2 relative toownship 1 at time ti and representatively shown asangle 50′ inFIG. 1 ; - tβ is the time at which θβ was measured;
- ti is the time at which θi was measured;
- Δt is the difference between two time measurements, e.g. Δtj,k is the difference between time tj and time tk;
- VREL is the difference velocity between
target 2 andownship 1; and - RCPA is the range to target 2 at CPA.
- θβ is as defined in equation (3) and representatively shown as
Min RCPA=Vos(tβ−ti)cos(θβ−θi)θ
tan(θi−θ0)=(ti−t0)(VR/RCPA) (4)
As used in equation (4),
-
- θ0 is the angle between
ownship 1's heading andtarget 2 at an initial time t0; - θi is the angle between
ownship 1's heading andtarget 2 at time ti; - ti is the time of bearing reading θi; and
- t0 is the time of bearing reading θ0.
Further, the ratio VR/RCPA is a calculated value, and therefore VR may be estimated based on an estimated value of RCPA. Alternatively, RCPA may be estimated based on an estimated value of VR.
- θ0 is the angle between
Min RCPA=Vos(tβ−t0)cos(θβ−θ0) (5)
In equation (5),
-
- tβ is the time at which θβ was measured;
- t0 is the time of bearing reading θ0;
- Vos is magnitude of the velocity of ownship; and
- θ0 is the angle between
ownship 1′s heading andtarget 2 at a time ti=0.
RCPA
where
-
- ΔtCC is the difference between course crossings, course crossings being defined as the time when
ownship 1 crosses thetarget 2's course and to and the other components have the definitions given above.
- ΔtCC is the difference between course crossings, course crossings being defined as the time when
In equation (7),
-
- θi is the angle between
ownship 1's heading andtarget 2 at time ti; - θj is the angle between
ownship 1's heading andtarget 2 at time tj; - θk is the angle between
ownship 1′s heading andtarget 2 at time tk; and - Δtα,β is the time difference between measurements θα, θβ respectively, i.e., where α and β are generic indices which are respectively pair-wise, i.e. (j,k), (k,i), and (i,j).
- θi is the angle between
In equation (8),
-
- θβ is the BRG at CPA;
- θi is the angle between
ownship 1's heading andtarget 2 at time ti; - θj is the angle between
ownship 1's heading andtarget 2 at time tj; and - Δti,j is the time difference between measurements θi and θj.
In equation (9),
-
- θβ is the angle between
ownship 1's heading andtarget 2 at CPA; - θi is the angle between
ownship 1's heading andtarget 2 at time ti; - ti is the time of bearing reading θi; and
- tβ is the time of bearing reading θβ, time at which CPA occurs.
- θβ is the angle between
MinRCPA=Vos(tβ−ti)cos(θβ−θi)θ
In equation (10),
-
- θβ is the angle between
ownship 1's heading andtarget 2 at CPA; - θi is the angle between
ownship 1's heading andtarget 2 at time ti; - Vos is a magnitude of ownship's velocity;
- ti is time of bearing reading θi; and
- tβ is the is the time at which θβ was measured.
- θβ is the angle between
Min Rest=Min. RCPA/cos(θβ−θj)|θj=current bearing measure (11)
where the terms in equation (11) are defined above.
R(CURRENTMINIMUM)=RCPA(MINIMUM)/cos(θ0−θi) (14)
Claims (83)
Min RCPA=VOS(tβ−ti)cos(θβ−θi)θ
Min RCPA=Vos(tβ−ti)cos(θβ−θi)θ
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US11/318,398 USRE42546E1 (en) | 2002-03-27 | 2005-12-22 | Method and system for target localization |
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US10/108,236 US6668218B1 (en) | 2002-03-27 | 2002-03-27 | Method and system for target localization |
US11/318,398 USRE42546E1 (en) | 2002-03-27 | 2005-12-22 | Method and system for target localization |
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